Ortak Dersler Bölümü

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A New Estimation Technique for AR(1) Model with Long-Tailed Symmetric Innovations
(2017) Dener Akkaya, Ayşen; Türker Bayrak, Özlem; 56416
In recent years, it is seen in many time series applications that innovations are non-normal. In this situation, it is known that the least squares (LS) estimators are neither efficient nor robust and maximum likelihood (ML) estimators can only be obtained numerically which might be problematic. The estimation problem is considered newly through different distributions by the use of modified maximum likelihood (MML) estimation technique which assumes the shape parameter to be known. This becomes a drawback in machine data processing where the underlying distribution cannot be determined but assumed to be a member of a broad class of distributions. Therefore, in this study, the shape parameter is assumed to be unknown and the MML technique is combined with Huber’s estimation procedure to estimate the model parameters of autoregressive (AR) models of order 1, named as adaptive modified maximum likelihood (AMML) estimation. After the derivation of the AMML estimators, their efficiency and robustness properties are discussed through simulation study and compared with both MML and LS estimators. Besides, two test statistics for significance of the model are suggested. Both criterion and efficiency robustness properties of the test statistics are discussed, and comparisons with the corresponding MML and LS test statistics are given. Finally, the estimation procedure is generalized to AR(q) models.
A New Estimation Technique for AR(1) Model with Long-Tailed Symmetric Innovations
(Springer, 2018) Dener Akkaya, Ayşen; Türker Bayrak, Özlem; 56416
In recent years, it is seen in many time series applications that innovations are non-normal. In this situation, it is known that the least squares (LS) estimators are neither efficient nor robust and maximum likelihood (ML) estimators can only be obtained numerically which might be problematic. The estimation problem is considered newly through different distributions by the use of modified maximum likelihood (MML) estimation technique which assumes the shape parameter to be known. This becomes a drawback in machine data processing where the underlying distribution cannot be determined but assumed to be a member of a broad class of distributions. Therefore, in this study, the shape parameter is assumed to be unknown and the MML technique is combined with Huber’s estimation procedure to estimate the model parameters of autoregressive (AR) models of order 1, named as adaptive modified maximum likelihood (AMML) estimation. After the derivation of the AMML estimators, their efficiency and robustness properties are discussed through simulation study and compared with both MML and LS estimators. Besides, two test statistics for significance of the model are suggested. Both criterion and efficiency robustness properties of the test statistics are discussed, and comparisons with the corresponding MML and LS test statistics are given. Finally, the estimation procedure is generalized to AR(q) models.
Adaptive Estimation of Autoregressive Models Under Long-Tailed Symmetric Distribution
(Association for Computing Machinery, 2019) Yengür, Begüm; Bayrak, Özlem Türker; Dener Akkaya, Ayşen; 56416
In this paper, we consider the autoregressive models where the error term is non-normal; specifically belongs to a long-tailed symmetric distribution family since it is more relevant in practice than the normal distribution. It is known that least squares (LS) estimators are neither efficient nor robust under non-normality and maximum likelihood (ML) estimators cannot be obtained explicitly and require a numerical solution which might be problematic. In recent years, modified maximum likelihood (MML) estimation is developed to overcome these difficulties. However, this method requires that the shape parameter is known which is not realistic in machine data processing. Therefore, we use adaptive modified maximum likelihood (AMML) technique which combines MML with Huber’s estimation procedure so that the shape parameter is also estimated. After derivation of the AMML estimators, their efficiency and robustness properties are discussed through a simulation study and compared with MML and LS estimators.
Classification Models Based On Tanaka's Fuzzy Linear Regression Approach: the Case of Customer Satisfaction Modeling
(IOS Press, 2010) Bayrak, Özlem Türker; 56416
Fuzzy linear regression (FLR) approaches are widely used for modeling relations between variables that involve human judgments, qualitative and imprecise data. Tanaka's FLR analysis is the first one developed and widely used for this purpose. However, this method is not appropriate for classification problems, because it can only handle continuous type dependent variables rather than categorical. In this study, we propose three alternative approaches for building classification models, for a customer satisfaction survey data, based on Tanaka's FLR approach. In these models, we aim to reflect both random and fuzzy types of uncertainties in the data in different ways, and compare their performances using several classification performance measures. Thus, this study contributes to the field of fuzzy classification by developing Tanaka based classification models.
Effect of Estimation on Simple Linear Profile Monitoring under Non-normality
(2019) Aytaçoğlu, Burcu; Türker Bayrak, Özlem; 56416
In recent years, many control charts have been proposed to monitor profiles where the quality of a process/product is expressed as function of response and explanatory variable(s). The methods mostly assume that the in control parameter values are known in Phase II analysis and innovations are normally distributed. However, in practice, the parameters are estimated in Phase I analysis and innovations may be non-normal. In this study, the performance of T2, EWMA-R and EWMA-3 methods for monitoring simple linear profiles is examined via simulation where the parameters are estimated and innovations have Student’s t-distribution. As a performance measure, both the average and standard deviation of the run length is considered. Finally, some recommendations for practitioners are summarized in a table.
Effect of estimation under nonnormality on the phase II performance of linear profile monitoring approaches
(Wiley, 2019) Aytaçoğlu, Burcu; Bayrak, Özlem Türker; 56416
The number of studies about control charts proposed to monitor profiles, where the quality of a process/product is expressed as function of response and explanatory variable(s), has been increasing in recent years. However, most authors assume that the in-control parameter values are known in phase II analysis and the error terms are normally distributed. These assumptions are rarely satisfied in practice. In this study, the performance of EWMA-R, EWMA-3, and EWMA-3(d(2)) methods for monitoring simple linear profiles is examined via simulation where the in-control parameters are estimated and innovations have a Student's t distribution or gamma distribution. Instead of the average run length (ARL) and the standard deviation of run length, we used average and standard deviation of the ARL as performance measures in order to capture the sampling variation among different practitioners. It is seen that the estimation effect becomes more severe when the number of phase I profiles used in estimation decreases, as expected, and as the distribution deviates from normality to a greater extent. Besides, although the average ARL values get closer to the desired values as the amount of phase I data increases, their standard deviations remain far away from the acceptable level indicating a high practitioner-to-practitioner variability.
Electricity Price Modelling for Turkey
(Springer-Verlag Berlin, 2012) Yıldırım, Miray Hanım; Bayrak, Özlem Türker; Weber, Gerhard Wilhelm; Özmen, Ayşe; 56416
This paper presents customized models to predict next-day's electricity price in short-term periods for Turkey's electricity market. Turkey's electricity market is evolving from a centralized approach to a competitive market. Fluctuations in the electricity consumption show that there are three periods; day, peak, and night. The approach proposed here is based on robust and continuous optimization techniques, which ensures achieving the optimum electricity price to minimize error in periodic price prediction. Commonly, next-day's electricity prices are forecasted by using time series models, specifically dynamic regression model. Therefore electricity price prediction performance was compared with dynamic regression. Numerical results show that CMARS and RCMARS predicts the prices with 30% less error compared to dynamic regression.
Estimation of AR(1) Model Having Generalized Logistic Disturbances
(2020) Akkaya, Ayşen; Türker Bayrak, Özlem; 56416
Non-normality is becoming a common feature in real life applications. Using non-normal disturbances in autoregressive models induces non-linearity in the likelihood equations so that maximum likelihood estimators cannot be derived analytically. Thus, modified maximum likelihood estimation (MMLE) technique is introduced in literature to overcome this difficulty. However, this method assumes the shape parameter to be known which is not realistic in real life. Recently, for unknown shape parameter case, adaptive modified maximum likelihood estimation (AMMLE) method that combines MMLE with Huber estimation method is suggested in literature. In this study, we adopt AMMLE method to AR(1) model where the disturbances are Generalized Logistic distributed. Although Huber M-estimation is not applicable to skew distributions, the AMMLE method extends Huber type work to skew distributions. We derive the estimators and evaluate their performance in terms of effici
Forecasting The Natural Gas Demand At New Locations A Case Study For Turkey
(2005) Türker Bayrak, Özlem; Köksal, Gülser; Okandan, Ender; 56416
Global Krizler için Doğrusal Profillere Dayalı Kontrol Şemaları ile Oluşturulan Erken Uyarı Sistemi
(2015) Türker Bayrak, Özlem; Aytaçoğlu, Burcu; Yüksel Haliloğlu, Ebru; 56416
Inference of Autoregressive Model with Stochastic Exogenous Variable Under Short-Tailed Symmetric Distributions
(Springer International Publishing AG, 2018) Bayrak, Özlem Türker; Dener Akkaya, Ayşen; 56416
In classical autoregressive models, it is assumed that the disturbances are normally distributed and the exogenous variable is non-stochastic. However, in practice, short-tailed symmetric disturbances occur frequently and exogenous variable is actually stochastic. In this paper, estimation of the parameters in autoregressive models with stochastic exogenous variable and non-normal disturbances both having short-tailed symmetric distribution is considered. This is the first study in this area as known to the authors. In this situation, maximum likelihood estimation technique is problematic and requires numerical solution which may have convergence problems and can cause bias. Besides, statistical properties of the estimators can not be obtained due to non-explicit functions. It is also known that least squares estimation technique yields neither efficient nor robust estimators. Therefore, modified maximum likelihood estimation technique is utilized in this study. It is shown that the estimators are highly efficient, robust to plausible alternatives having different forms of symmetric short-tailedness in the sample and explicit functions of data overcoming the necessity of numerical solution. A real life application is also given.
Inter-laboratory comparison scheme for fuel sector, LABKAR in Turkey
(Springer, 2009) Bayrak, Özlem Türker; Okandan, Ender; Üçkardeş, Hale; 56416
Fuel sector is one of the powerful sectors in Turkish industry. The implementation of a new law for regulating the fuel sector had enforced the quality control of fuels sold to public. This resulted in several accredited fuel-testing laboratories to emerge. Thus, a scheme to evaluate their proficiency in measurements became an important requirement. The inter-laboratory comparison scheme LABKAR for gasoline, diesel oil, LPG, lubricating oil and biodiesel samples have evolved to fulfill this need. In this paper, LABKAR is introduced; the results obtained from the program are analyzed and discussed. The kernel densities of the participants' results show that the use of robust mean as a consensus value is appropriate for fuel samples. Although the number of rounds is not enough to derive strict conclusions, it is seen that the performance of the scheme based on the standard deviations and coefficient of variations is improving in each round. It has been observed that the number of laboratories receiving "action" or "warning" is decreasing, which indicates that they are benefiting from the scheme.
Linear contrasts in one-way classification AR(1) model with gamma innovations
(Hacettepe Univ, Fac Sci, 2016) Şenoğlu, Birdal; Bayrak, Özlem Türker; 56416
In this study, the explicit estimators of the model parameters in oneway classification AR(1) model with gamma innovations are derived by using modified maximum likelihood (MML) methodology. We also propose a new test statistic for testing linear contrasts. Monte Carlo simulation results show that the MML estimators have higher efficiencies than the traditional least squares (LS) estimators and the proposed test has much better power and robustness properties than the normal theory test.
Linear Profile Monitoring Adapted to Construct Early Warning System in Economics: A Pilot Study From Energy Sector
(2019) Türker Bayrak, Özlem; Aytaçoğlu, Burcu; Yüksel Haliloğlu, Ebru; 56416
In this study, control charts for monitoring linear profiles are adopted to early warning system (EWS) to see if global crises can be detected before they occur so that preventive actions can be taken by the policy makers. For this purpose, the relation between the annual gross domestic product (GDP) and energy consumption of G8 and big emerging countries through the years 1980-2012 is observed. Phase I analysis indicated that the model parameters are autocorrelated through time. Thus, the Shewhart and EWMA charts for linear profile monitoring are adopted to take this into account and found that EWMA is better. It is seen that the 2008 global crisis can be detected whereas relatively local Asian crisis cannot. This is the first study that integrates linear profile monitoring schemes to EWS and that takes into account the correlation among profiles with different explanatory variables (x-values) for each profile.
Survey and evaluation on modelling of next-day electricity prices
(2014) Yıldırım, Miray Hanım; Bayrak, Özlem Türker; Weber, Gerhard-Wilhelm; 56416

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